Contrasting Metallic (Rh0) and Carbidic (2D-Mo2C MXene) Surfaces in Olefin Hydrogenation Provides Insights on the Origin of the Pairwise Hydrogen Addition

Kinetic studies are vital for gathering mechanistic insights into heterogeneously catalyzed hydrogenation of unsaturated organic compounds (olefins), where the Horiuti–Polanyi mechanism is ubiquitous on metal catalysts. While this mechanism envisions nonpairwise H2 addition due to the rapid scrambling of surface hydride (H*) species, a pairwise H2 addition is experimentally encountered, rationalized here based on density functional theory (DFT) simulations for the ethene (C2H4) hydrogenation catalyzed by two-dimensional (2D) MXene Mo2C(0001) surface and compared to Rh(111) surface. Results show that ethyl (C2H5*) hydrogenation is the rate-determining step (RDS) on Mo2C(0001), yet C2H5* formation is the RDS on Rh(111), which features a higher reaction rate and contribution from pairwise H2 addition compared to 2D-Mo2C(0001). This qualitatively agrees with the experimental results for propene hydrogenation with parahydrogen over 2D-Mo2C1–x MXene and Rh/TiO2. However, DFT results imply that pairwise selectivity should be negligible owing to the facile H* diffusion on both surfaces, not affected by H* nor C2H4* coverages. DFT results also rule out the Eley–Rideal mechanism appreciably contributing to pairwise addition. The measurable contribution of the pairwise hydrogenation pathway operating concurrently with the dominant nonpairwise one is proposed to be due to the dynamic site blocking at higher adsorbate coverages or another mechanism that would drastically limit the diffusion of H* adatoms.

The red, black and blue lines represent the three modes of H adatom diffusion explored departing from any competitive hollow site minimum.

Section S2: Estimations of Rates
The non-activated adsorption rate of a species (rads) can be gained using collision theory, 2 as; where S0 is the initial sticking coefficient, pi the partial pressure of H2, C2H4, or C2H6 in the gas phase, and A represents the surface area of an adsorption site, estimated by dividing the surface supercell area, see Figure S1, by the number of possible adsorption sites.
The desorption rate, rdes, is estimated from the transition state theory (TST) and assuming that the desorbed TS is a late two-dimensional (2D) transition state, 3 where the energy barrier is the desorption energy, DE des i , which is simply a negative of the adsorption energy, DE ads i , see main text.Thus, viz.: where DE ads i is, here, non-ZPE corrected.Note that in such rates definitions, ZPE is accounted for in the vibrational partition function.Indeed, the pre-factor  $"A is given by various partition functions, , including those in Equations (10-12). .'#FA,U" The  .'#FA,U""#A ,  '/."#A , and  -2C "#A refer to the gas phase translational partition function including just 2D degrees of freedom (as the third dimension is the reaction coordinate for desorption), the rotational partition function, and the vibrational partition function, respectively, computed in a large box.The  -2C #$A is the vibrational partition function of the adsorbed molecule where six degrees of freedom correspond to frustrated rotations and translations, vide supra.Finally, for the rotational partition functions, see Eq. (S8), Trot is the rotational temperature of the adsorbed species.
For the reactive and diffusive steps, the corresponding rates,  ž , have been obtained as well by TST, 4 defined as: where ∆ ]} represents the non-ZPE corrected energy barrier, the pre-factor for  can be determined by the partition function, which refers to the vibrational partition functions in the initial state (IS) or the transition state (TS) on the surface;  -2C ]}/{} denotes the vibrational partition given by:

Section S3: The Span Model
The energy span model has been widely used to assess activity beyond traditional methods, which consider all individual transition states. 5,6Within the span model, the ratedetermining transition state (RDTS) is identified as the transition state with the highest energy, which influences the reaction rate significantly.The rate-determining intermediate (RDI), i.e., the one with the lowest energy, is used to seize the energy span. 7e span energy barrier,  C A^#F , captures the energetic requirement of the reaction, defined as: ¡"]} −  0/¢"A.
Further details on the applicability of the span model are found in the literature.Table S3.H2 adsorption energies on ABA-Mo2C, ABC-Mo2C, and Rh surface models with different relative sites with respect to pre-adsorbed C2H4 as specified in Figure S6.
All values are given in eV.The bold font represents the ones selected to study H2 dissociation forward.S7).

Figure S1 .
Figure S1.Top (upper images) and side (lower images) views of p(4×4) MXene-derived 2D-Mo2C (0001) surface with (a) ABA stacking and (b) ABC stacking, as well as (c) Rh (111) surface.High symmetry sites are specified, including top (T) and bridge (B) sites for all surface models, hollow carbon (HC), hollow blank (HB), and hollow metal (HM) for ABA-and ABC-stacked 2D-Mo2C (0001), and hexagonal close-packed hollow (Hhcp) and face-centred cubic hollow (Hfcc) on Rh (111).C and H atoms are represented by brown and white spheres, respectively, while Mo and Rh atoms are shown as pinkish and greenish spheres, with different levels of shading depending on their stacking position.

Figure S4 .
Figure S4.The lowest-energy high-symmetry surface sites of two vicinal H adatoms on (a) ABA-Mo2C and (b) ABC-Mo2C (0001) surfaces, and (c) Rh (111) surface.Numbered circles represent the potential high-symmetry positions for the second H adatom, while orange circles represent the final most stable positions.

Figure S6 .
Figure S6.The lowest-energy co-adsorption sites of H2 nearby of the adsorbed C2H4* on (a) ABA-Mo2C, (b) ABC-Mo2C, and (c) Rh (111) surfaces.Numbered circles represent potential high-symmetry positions for the co-adsorption of H2, while orange circles represent the final most stable positions.

Figure S7 .
Figure S7.The main high-symmetry surface sites for the H2 adsorption and two vicinal H* adatoms produced as a result of the H2 dissociation on (a) ABA-Mo2C-1 and ABA-Mo2C-2, (b) ABC-Mo2C-1 and ABC-Mo2C-2, and (c) Rh-1, Rh-2, and Rh-3 surfaces in the presence of C2H4.For details on the notations used, see Figure S6.

Figure S14 .
Figure S14.Top views of the IS, TS, and MS of H diffusion on (a) ABA-Mo2C, (b) ABC-Mo2C, and (c) Rh (111) surface models with ¾ ML of C2H4*.Notice that because of symmetry, the final diffusion from MS to FS is the same as from IS to MS.

Figure S15 .
Figure S15.Top views of the IS, TS, and MS of H diffusion on (a) ABA-Mo2C, (b) ABC-Mo2C, and (c) Rh (111) surface models with ¾ ML of H*.Notice that because of symmetry, the final diffusion from MS to FS is the same as from IS to MS.
represent the total energy, and the zero point energy (ZPE) contributions of the adsorbed species, and that species in vacuum, respectively. 3 , for instance, would be the number of metal atoms, e.g. in the Rh (111) slab model, while for  2 the mass of the i th molecule,  2 denotes the partial pressure of the i th species,  2 AwW is the symmetry number of i th molecule -2 for H2, 4 for C2H4, and 6 for C2H6, 1  y,2 is the rotational constant, computed as  y,2 = the Mo2C models, this would be the number of each of substrate atom types.Since the number of substrate atoms is invariant in our study,  ./.#0 ( 2 ,  3 ) =  2/ABC , and  ./.#0 (0,  3 ) =  ABC , where Esub and Ei/sub are the total energies of the pristine surface model and of the surface model with the i th species adsorbed upon, respectively.Aside, ∆ 2 (, ) is the chemical potential change of the adsorbed species with respect to the gas phase, where details on how to estimate it are provided below. 2 89: can be obtained from vibrational frequencies, viz.:where h is the Planck's constant, and  F is the vibrational frequency for each normal mode n of vibration (NMV), i.e., 3N−5 for linear molecules in vacuum, 3N−6 for nonlinear molecules in vacuum, and 3N for adsorbed atoms/molecules, where N is the number of atoms (taking into account the loss of free translations and rotations that are effectively converted into vibrations upon adsorption).For C2H4, C2H6, and H2 molecules, the gas reference is well-defined.For radical species such as C2H5 and H adatoms it is convenient 7,8

Table S2 .
Adsorption energies of two H adatoms on ABA-and ABC-Mo2C and Rh surfaces on different sites as specified in FigureS4.All values are given in eV, and do not include the ZPE term.The bold font represents the lowest energy case.

Table S8 .
Energy barriers, Eb, for H diffusion and H2 dissociation on ABA-Mo2C, ABC-Mo2C, and Rh surfaces, when pristine or in the presence C2H4, plus the H2 adsorption energies.All values are given in eV.

Table S9 .
Reaction energies, ΔE, and energy barriers, Eb, of the first and second hydrogenation reaction steps on C2H4, as well as the full DE and the energy barrier according to the span model,  C A^#F , on the ABA-and ABC-Mo2C surface models depicted in Figure 3 of the main text, and on Rh (111).All values are given in eV.

Table S10 .
Reaction energies, ΔE, and energy barriers, Eb, of the first and second hydrogenation reaction steps on C2H4, as well as the full ∆ A^#F and the energy barrier according to the span model,  C A^#F , on the ABA-and ABC-Mo2C surface models, and on Rh (111) surface, either on their pristine models, or having ¾ ML of H or C2H4 depicted in Figures S11-S13.

Table S11 .
Energy barriers, Eb, for H diffusion on ABA-Mo2C, ABC-Mo2C, and Rh surfaces, either on their pristine models, or having ¾ ML of H or C2H4 depicted in Figure4.All values are given in eV.